For a summand \(\mathbb {F}[U]/U^{n_i}\)  consider its top and bottom elements; these have a difference in grading of \(2n_i-2\) . Denote by \(x_{\pm }\)  cycles representing these two elements; these are not represented by reducible generators, as otherwise they would belong to the \(U\) -tower (cf. [1]}). Then
\(2n_i-2=\mathrm {gr}(x_+,x_-)=\mathrm {gr}(x_+,[\mathfrak {b}_0])+\mathrm {gr}([\mathfrak {b}_0],x_-)\le |\mathrm {gr}(x_+,[\mathfrak {b}_0])|+|\mathrm {gr}([\mathfrak {b}_0],x_-)|\) 
and the result follows from ().
